I want to make a small coop that, with an attached run, can be moved from bed to bed, so the birds directly manure the ground beneath between plantings.

It needs to be light enough to be moved easily by two people, so the smaller the better really. We're in a temperate European climate, so the birds will really only come into the coop to roost and to lay.

How far off the ground should the perch (roost) be? And how much headroom is needed above it?

I plan to do the same type of thing. But, I'm doing it a little backwards from you. I've built my tractor (4x10+4) and then I'm building a 30x5 raised bed box. I plan to move the tractor inside of the grow box.